EllipsoideSurveying · Land tenure · Geodesy
FRENعربيةالدارجة
Request a quote

Free tool

Surveying calculations.

Bearing and distance between two points, radiation, angle conversions, slopes and earthwork volumes: a surveyor's everyday calculations, using Moroccan conventions (Lambert grid, bearings measured from north in gons). Everything is computed in your browser: nothing is sent.

Calculations run on your device; no data is transmitted. Your last entries are kept in this browser ("Clear my entries" button at the bottom of the tool).

Distance and bearing

Enter the plane coordinates of two points (X to the east, Y to the north, in metres, for example Lambert). Add elevations to also get the height difference, slope distance and gradient.

Start point A
End point B
Reducing a Lambert distance to the ground

A distance computed from Lambert coordinates is a distance on the projection plane. The horizontal distance measured on the ground differs from it, often by several centimetres and up to a few tens of centimetres per kilometre: the projection slightly distorts lengths (scale factor) and the ground lies above the ellipsoid (elevation). Tick the box to get the ground distance.

If left empty: mean of the elevations of A and B when entered, otherwise 0 m.

For the area and perimeter of a plot from the coordinates of its boundary markers, use our dedicated tool: land area calculator.

Empties all fields and forgets the entries kept in this browser.

Conventions

The conventions used by the tool.

They are those of Moroccan surveying, inherited from the French school: plane coordinates with X to the east and Y to the north (Lambert Morocco projection), grid bearing measured clockwise from grid north, angles in gons (400 gon per turn), zenith angle zero at the zenith and 100 gon when horizontal.

The bearing from A to B is G = arctan(ΔX ÷ ΔY), taking the quadrant into account (signs of ΔX and ΔY); the horizontal distance is √(ΔX² + ΔY²). Radiation applies the reverse: X = Xs + D × sin G and Y = Ys + D × cos G.

  • Quadrant 1: ΔX ≥ 0 and ΔY > 0, bearing from 0 to 100 gon
  • Quadrant 2: ΔX > 0 and ΔY ≤ 0, bearing from 100 to 200 gon
  • Quadrant 3: ΔX ≤ 0 and ΔY < 0, bearing from 200 to 300 gon
  • Quadrant 4: ΔX < 0 and ΔY ≥ 0, bearing from 300 to 400 gon

The parameters of the Lambert Morocco projections (zones I to IV, Clarke 1880 ellipsoid) are those of the EPSG geodetic registry, for example [EPSG:26191 — Merchich / Nord Maroc](https://epsg.org/crs_26191/Merchich-Nord-Maroc.html). The scale factor and convergence computed by the tool have been checked against the PROJ reference library.

Methods

How the volumes are computed.

Two earthwork methods, chosen according to the shape of the project. Both give in-place volumes: bulking of excavated material (optional) and settlement of fill depend on the soil and are not guessed by the tool.

Grid (platforms, plots)

The site is covered by a regular grid; at each node the existing ground level and the design level are known. The height h = ground − design gives cut (h > 0) or fill (h < 0).

  • Triangular prisms: each cell is split into two triangles; the volume of a triangle is its area × the mean of its three heights, and the cut part of a mixed triangle is computed exactly.
  • Rectangular prisms: V = S/4 × (h1 + h2 + h3 + h4) per cell, i.e. S/4 × (Σh₁ + 2Σh₂ + 3Σh₃ + 4Σh₄) for a whole grid; the classic approximation in mixed cells.
  • The tool shows the result of the other method as a check: a large difference means the grid is too coarse.

Cross-sections (roads, tracks, canals)

On each cross-section, the cut area and the fill area are measured; sections are separated by a known distance along the centreline.

  • Average end area: V = d × (S1 + S2) ÷ 2 for each stretch, separately for cut and fill.
  • Transition section: between an all-cut and an all-fill section, the transition point is placed at d × Sc ÷ (Sc + Sf) so that neither volume is overestimated.
  • Prismoidal (Simpson): with equally spaced sections and an even number of intervals, V = d ÷ 3 × (S0 + 4 S1 + 2 S2 + … + Sn).

Limits

Exact calculations on data that must be checked.

The formulas are exact and tested; the result depends entirely on the coordinates, angles, levels and areas you enter. Volumes computed on a coarse grid or approximate levels remain an estimate.

The tool replaces neither a topographic survey, nor a setting-out, nor a joint measurement of works. For a file, a public contract or a dispute, measurements and calculations must be carried out and signed by a licensed surveyor (ingénieur géomètre-topographe).

Frequently asked questions

Understanding surveying calculations.

What is the difference between grid bearing and azimuth?

The grid bearing is measured from the north of the map grid (the Y axis of the Lambert projection); the true azimuth from true north, along the meridian. The difference is the meridian convergence: zero on the central meridian (5.4° W), it reaches about 0.2° in Fez and more than one degree at the edges of the zones. The magnetic azimuth, that of a compass, differs again by the magnetic declination.

Why use gons rather than degrees?

In Morocco, as in France, surveyors mostly work in gons and set their instruments (total stations, theodolites) accordingly: a right angle is 100 gon and a half turn 200 gon, which simplifies back bearings and quadrants. The tool also accepts decimal degrees and degrees-minutes-seconds.

My computed distance differs from the one measured with a tape or a rangefinder: why?

A distance computed from Lambert coordinates is a distance on the projection plane. It differs from the distance measured on the ground, by a few centimetres to a few tens of centimetres per kilometre depending on the location (projection scale factor) and the elevation. Open "Reducing a Lambert distance to the ground" in the Distance tab to get the ground distance. A tape measurement adds its own errors (tension, slope, alignment).

Which volume method should I choose?

The grid suits platforms and plots (earthworks for a lot, a building, a car park); cross-sections suit long works (road, track, canal, trench). In both cases, the closer the grid or the sections, the more accurate the volume.

Is a bulking factor provided?

No. It depends on the type of soil (topsoil, clay, rock…) and is set by a geotechnical study or by the contract specifications. The tool applies it only if you enter it.

How do I calculate the area of a plot?

With our land area calculator: it computes area and perimeter from the coordinates of the boundary markers, from a drawing on the map, or from tape measurements.

Is my data sent anywhere?

No. All calculations run in your browser. Your last entries are kept only on your device; the "Clear my entries" button deletes them.

Need reliable measurements?

Surveys, setting-out and earthwork volumes on site.

Total station, GNSS tied to the geodetic network, spot-height plans, cross-sections and earthwork quantities: we measure and compute for your projects in the Fès-Meknès region.

Request a quote Call the office
Address
47, avenue des FAR, 3e étage, appartement 5, Ville Nouvelle
30050 Fès

Google Maps ↗Apple Maps ↗Google profile ↗